{- |
Module      :  Crystallography.HallSymbols.SpacegroupSymbols
Copyright   :  (c) Jun Narumi 2018
License     :  BSD3 (see the LICENSE file)

Maintainer  :  narumij@gmail.com
Stability   :  experimental
Portability :  ?

Spacegroup Symbols

[References]

1. Concise Space-Group Symbols http://cci.lbl.gov/sginfo/hall_symbols.html , See also : https://github.com/rwgk/sginfo

2. ITVB 2001 Table A1.4.2.7 Hall symbols http://cci.lbl.gov/sginfo/itvb_2001_table_a1427_hall_symbols.html

-}
module Crystallography.HallSymbols.SpacegroupSymbols (
  spacegroupSymbols,
  NumberAndChoice,
  HMFull,
  HallName
  ) where

type NumberAndChoice = String
type HMFull = String
type HallName = String

-- | Table 6. Concise space-group symbols
spacegroupSymbols :: [(NumberAndChoice,HMFull,HallName)]
spacegroupSymbols = [
  (  "1",  "P 1",  "P 1"  ),
  (  "2",  "P -1",  "-P 1"  ),
  (  "3:b",  "P 1 2 1",  "P 2y"  ),
  (  "3:c",  "P 1 1 2",  "P 2"  ),
  (  "3:a",  "P 2 1 1",  "P 2x"  ),
  (  "4:b",  "P 1 21 1",  "P 2yb"  ),
  (  "4:c",  "P 1 1 21",  "P 2c"  ),
  (  "4:a",  "P 21 1 1",  "P 2xa"  ),
  (  "5:b1",  "C 1 2 1",  "C 2y"  ),
  (  "5:b2",  "A 1 2 1",  "A 2y"  ),
  (  "5:b3",  "I 1 2 1",  "I 2y"  ),
  (  "5:c1",  "A 1 1 2",  "A 2"  ),
  (  "5:c2",  "B 1 1 2",  "B 2"  ),
  (  "5:c3",  "I 1 1 2",  "I 2"  ),
  (  "5:a1",  "B 2 1 1",  "B 2x"  ),
  (  "5:a2",  "C 2 1 1",  "C 2x"  ),
  (  "5:a3",  "I 2 1 1",  "I 2x"  ),
  (  "6:b",  "P 1 m 1",  "P -2y"  ),
  (  "6:c",  "P 1 1 m",  "P -2"  ),
  (  "6:a",  "P m 1 1",  "P -2x"  ),
  (  "7:b1",  "P 1 c 1",  "P -2yc"  ),
  (  "7:b2",  "P 1 n 1",  "P -2yac"  ),
  (  "7:b3",  "P 1 a 1",  "P -2ya"  ),
  (  "7:c1",  "P 1 1 a",  "P -2a"  ),
  (  "7:c2",  "P 1 1 n",  "P -2ab"  ),
  (  "7:c3",  "P 1 1 b",  "P -2b"  ),
  (  "7:a1",  "P b 1 1",  "P -2xb"  ),
  (  "7:a2",  "P n 1 1",  "P -2xbc"  ),
  (  "7:a3",  "P c 1 1",  "P -2xc"  ),
  (  "8:b1",  "C 1 m 1",  "C -2y"  ),
  (  "8:b2",  "A 1 m 1",  "A -2y"  ),
  (  "8:b3",  "I 1 m 1",  "I -2y"  ),
  (  "8:c1",  "A 1 1 m",  "A -2"  ),
  (  "8:c2",  "B 1 1 m",  "B -2"  ),
  (  "8:c3",  "I 1 1 m",  "I -2"  ),
  (  "8:a1",  "B m 1 1",  "B -2x"  ),
  (  "8:a2",  "C m 1 1",  "C -2x"  ),
  (  "8:a3",  "I m 1 1",  "I -2x"  ),
  (  "9:b1",  "C 1 c 1",  "C -2yc"  ),
  (  "9:b2",  "A 1 n 1",  "A -2yac"  ),
  (  "9:b3",  "I 1 a 1",  "I -2ya"  ),
  (  "9:-b1",  "A 1 a 1",  "A -2ya"  ),
  (  "9:-b2",  "C 1 n 1",  "C -2ybc"  ),
  (  "9:-b3",  "I 1 c 1",  "I -2yc"  ),
  (  "9:c1",  "A 1 1 a",  "A -2a"  ),
  (  "9:c2",  "B 1 1 n",  "B -2bc"  ),
  (  "9:c3",  "I 1 1 b",  "I -2b"  ),
  (  "9:-c1",  "B 1 1 b",  "B -2b"  ),
  (  "9:-c2",  "A 1 1 n",  "A -2ac"  ),
  (  "9:-c3",  "I 1 1 a",  "I -2a"  ),
  (  "9:a1",  "B b 1 1",  "B -2xb"  ),
  (  "9:a2",  "C n 1 1",  "C -2xbc"  ),
  (  "9:a3",  "I c 1 1",  "I -2xc"  ),
  (  "9:-a1",  "C c 1 1",  "C -2xc"  ),
  (  "9:-a2",  "B n 1 1",  "B -2xbc"  ),
  (  "9:-a3",  "I b 1 1",  "I -2xb"  ),
  (  "10:b",  "P 1 2/m 1",  "-P 2y"  ),
  (  "10:c",  "P 1 1 2/m",  "-P 2"  ),
  (  "10:a",  "P 2/m 1 1",  "-P 2x"  ),
  (  "11:b",  "P 1 21/m 1",  "-P 2yb"  ),
  (  "11:c",  "P 1 1 21/m",  "-P 2c"  ),
  (  "11:a",  "P 21/m 1 1",  "-P 2xa"  ),
  (  "12:b1",  "C 1 2/m 1",  "-C 2y"  ),
  (  "12:b2",  "A 1 2/m 1",  "-A 2y"  ),
  (  "12:b3",  "I 1 2/m 1",  "-I 2y"  ),
  (  "12:c1",  "A 1 1 2/m",  "-A 2"  ),
  (  "12:c2",  "B 1 1 2/m",  "-B 2"  ),
  (  "12:c3",  "I 1 1 2/m",  "-I 2"  ),
  (  "12:a1",  "B 2/m 1 1",  "-B 2x"  ),
  (  "12:a2",  "C 2/m 1 1",  "-C 2x"  ),
  (  "12:a3",  "I 2/m 1 1",  "-I 2x"  ),
  (  "13:b1",  "P 1 2/c 1",  "-P 2yc"  ),
  (  "13:b2",  "P 1 2/n 1",  "-P 2yac"  ),
  (  "13:b3",  "P 1 2/a 1",  "-P 2ya"  ),
  (  "13:c1",  "P 1 1 2/a",  "-P 2a"  ),
  (  "13:c2",  "P 1 1 2/n",  "-P 2ab"  ),
  (  "13:c3",  "P 1 1 2/b",  "-P 2b"  ),
  (  "13:a1",  "P 2/b 1 1",  "-P 2xb"  ),
  (  "13:a2",  "P 2/n 1 1",  "-P 2xbc"  ),
  (  "13:a3",  "P 2/c 1 1",  "-P 2xc"  ),
  (  "14:b1",  "P 1 21/c 1",  "-P 2ybc"  ),
  (  "14:b2",  "P 1 21/n 1",  "-P 2yn"  ),
  (  "14:b3",  "P 1 21/a 1",  "-P 2yab"  ),
  (  "14:c1",  "P 1 1 21/a",  "-P 2ac"  ),
  (  "14:c2",  "P 1 1 21/n",  "-P 2n"  ),
  (  "14:c3",  "P 1 1 21/b",  "-P 2bc"  ),
  (  "14:a1",  "P 21/b 1 1",  "-P 2xab"  ),
  (  "14:a2",  "P 21/n 1 1",  "-P 2xn"  ),
  (  "14:a3",  "P 21/c 1 1",  "-P 2xac"  ),
  (  "15:b1",  "C 1 2/c 1",  "-C 2yc"  ),
  (  "15:b2",  "A 1 2/n 1",  "-A 2yac"  ),
  (  "15:b3",  "I 1 2/a 1",  "-I 2ya"  ),
  (  "15:-b1",  "A 1 2/a 1",  "-A 2ya"  ),
  (  "15:-b2",  "C 1 2/n 1",  "-C 2ybc"  ),
  (  "15:-b3",  "I 1 2/c 1",  "-I 2yc"  ),
  (  "15:c1",  "A 1 1 2/a",  "-A 2a"  ),
  (  "15:c2",  "B 1 1 2/n",  "-B 2bc"  ),
  (  "15:c3",  "I 1 1 2/b",  "-I 2b"  ),
  (  "15:-c1",  "B 1 1 2/b",  "-B 2b"  ),
  (  "15:-c2",  "A 1 1 2/n",  "-A 2ac"  ),
  (  "15:-c3",  "I 1 1 2/a",  "-I 2a"  ),
  (  "15:a1",  "B 2/b 1 1",  "-B 2xb"  ),
  (  "15:a2",  "C 2/n 1 1",  "-C 2xbc"  ),
  (  "15:a3",  "I 2/c 1 1",  "-I 2xc"  ),
  (  "15:-a1",  "C 2/c 1 1",  "-C 2xc"  ),
  (  "15:-a2",  "B 2/n 1 1",  "-B 2xbc"  ),
  (  "15:-a3",  "I 2/b 1 1",  "-I 2xb"  ),
  (  "16",  "P 2 2 2",  "P 2 2"  ),
  (  "17",  "P 2 2 21",  "P 2c 2"  ),
  (  "17:cab",  "P 21 2 2",  "P 2a 2a"  ),
  (  "17:bca",  "P 2 21 2",  "P 2 2b"  ),
  (  "18",  "P 21 21 2",  "P 2 2ab"  ),
  (  "18:cab",  "P 2 21 21",  "P 2bc 2"  ),
  (  "18:bca",  "P 21 2 21",  "P 2ac 2ac"  ),
  (  "19",  "P 21 21 21",  "P 2ac 2ab"  ),
  (  "20",  "C 2 2 21",  "C 2c 2"  ),
  (  "20:cab",  "A 21 2 2",  "A 2a 2a"  ),
  (  "20:bca",  "B 2 21 2",  "B 2 2b"  ),
  (  "21",  "C 2 2 2",  "C 2 2"  ),
  (  "21:cab",  "A 2 2 2",  "A 2 2"  ),
  (  "21:bca",  "B 2 2 2",  "B 2 2"  ),
  (  "22",  "F 2 2 2",  "F 2 2"  ),
  (  "23",  "I 2 2 2",  "I 2 2"  ),
  (  "24",  "I 21 21 21",  "I 2b 2c"  ),
  (  "25",  "P m m 2",  "P 2 -2"  ),
  (  "25:cab",  "P 2 m m",  "P -2 2"  ),
  (  "25:bca",  "P m 2 m",  "P -2 -2"  ),
  (  "26",  "P m c 21",  "P 2c -2"  ),
  (  "26:ba-c",  "P c m 21",  "P 2c -2c"  ),
  (  "26:cab",  "P 21 m a",  "P -2a 2a"  ),
  (  "26:-cba",  "P 21 a m",  "P -2 2a"  ),
  (  "26:bca",  "P b 21 m",  "P -2 -2b"  ),
  (  "26:a-cb",  "P m 21 b",  "P -2b -2"  ),
  (  "27",  "P c c 2",  "P 2 -2c"  ),
  (  "27:cab",  "P 2 a a",  "P -2a 2"  ),
  (  "27:bca",  "P b 2 b",  "P -2b -2b"  ),
  (  "28",  "P m a 2",  "P 2 -2a"  ),
  (  "28:ba-c",  "P b m 2",  "P 2 -2b"  ),
  (  "28:cab",  "P 2 m b",  "P -2b 2"  ),
  (  "28:-cba",  "P 2 c m",  "P -2c 2"  ),
  (  "28:bca",  "P c 2 m",  "P -2c -2c"  ),
  (  "28:a-cb",  "P m 2 a",  "P -2a -2a"  ),
  (  "29",  "P c a 21",  "P 2c -2ac"  ),
  (  "29:ba-c",  "P b c 21",  "P 2c -2b"  ),
  (  "29:cab",  "P 21 a b",  "P -2b 2a"  ),
  (  "29:-cba",  "P 21 c a",  "P -2ac 2a"  ),
  (  "29:bca",  "P c 21 b",  "P -2bc -2c"  ),
  (  "29:a-cb",  "P b 21 a",  "P -2a -2ab"  ),
  (  "30",  "P n c 2",  "P 2 -2bc"  ),
  (  "30:ba-c",  "P c n 2",  "P 2 -2ac"  ),
  (  "30:cab",  "P 2 n a",  "P -2ac 2"  ),
  (  "30:-cba",  "P 2 a n",  "P -2ab 2"  ),
  (  "30:bca",  "P b 2 n",  "P -2ab -2ab"  ),
  (  "30:a-cb",  "P n 2 b",  "P -2bc -2bc"  ),
  (  "31",  "P m n 21",  "P 2ac -2"  ),
  (  "31:ba-c",  "P n m 21",  "P 2bc -2bc"  ),
  (  "31:cab",  "P 21 m n",  "P -2ab 2ab"  ),
  (  "31:-cba",  "P 21 n m",  "P -2 2ac"  ),
  (  "31:bca",  "P n 21 m",  "P -2 -2bc"  ),
  (  "31:a-cb",  "P m 21 n",  "P -2ab -2"  ),
  (  "32",  "P b a 2",  "P 2 -2ab"  ),
  (  "32:cab",  "P 2 c b",  "P -2bc 2"  ),
  (  "32:bca",  "P c 2 a",  "P -2ac -2ac"  ),
  (  "33",  "P n a 21",  "P 2c -2n"  ),
  (  "33:ba-c",  "P b n 21",  "P 2c -2ab"  ),
  (  "33:cab",  "P 21 n b",  "P -2bc 2a"  ),
  (  "33:-cba",  "P 21 c n",  "P -2n 2a"  ),
  (  "33:bca",  "P c 21 n",  "P -2n -2ac"  ),
  (  "33:a-cb",  "P n 21 a",  "P -2ac -2n"  ),
  (  "34",  "P n n 2",  "P 2 -2n"  ),
  (  "34:cab",  "P 2 n n",  "P -2n 2"  ),
  (  "34:bca",  "P n 2 n",  "P -2n -2n"  ),
  (  "35",  "C m m 2",  "C 2 -2"  ),
  (  "35:cab",  "A 2 m m",  "A -2 2"  ),
  (  "35:bca",  "B m 2 m",  "B -2 -2"  ),
  (  "36",  "C m c 21",  "C 2c -2"  ),
  (  "36:ba-c",  "C c m 21",  "C 2c -2c"  ),
  (  "36:cab",  "A 21 m a",  "A -2a 2a"  ),
  (  "36:-cba",  "A 21 a m",  "A -2 2a"  ),
  (  "36:bca",  "B b 21 m",  "B -2 -2b"  ),
  (  "36:a-cb",  "B m 21 b",  "B -2b -2"  ),
  (  "37",  "C c c 2",  "C 2 -2c"  ),
  (  "37:cab",  "A 2 a a",  "A -2a 2"  ),
  (  "37:bca",  "B b 2 b",  "B -2b -2b"  ),
  (  "38",  "A m m 2",  "A 2 -2"  ),
  (  "38:ba-c",  "B m m 2",  "B 2 -2"  ),
  (  "38:cab",  "B 2 m m",  "B -2 2"  ),
  (  "38:-cba",  "C 2 m m",  "C -2 2"  ),
  (  "38:bca",  "C m 2 m",  "C -2 -2"  ),
  (  "38:a-cb",  "A m 2 m",  "A -2 -2"  ),
  (  "39",  "A b m 2",  "A 2 -2c"  ),
  (  "39:ba-c",  "B m a 2",  "B 2 -2c"  ),
  (  "39:cab",  "B 2 c m",  "B -2c 2"  ),
  (  "39:-cba",  "C 2 m b",  "C -2b 2"  ),
  (  "39:bca",  "C m 2 a",  "C -2b -2b"  ),
  (  "39:a-cb",  "A c 2 m",  "A -2c -2c"  ),
  (  "40",  "A m a 2",  "A 2 -2a"  ),
  (  "40:ba-c",  "B b m 2",  "B 2 -2b"  ),
  (  "40:cab",  "B 2 m b",  "B -2b 2"  ),
  (  "40:-cba",  "C 2 c m",  "C -2c 2"  ),
  (  "40:bca",  "C c 2 m",  "C -2c -2c"  ),
  (  "40:a-cb",  "A m 2 a",  "A -2a -2a"  ),
  (  "41",  "A b a 2",  "A 2 -2ac"  ),
  (  "41:ba-c",  "B b a 2",  "B 2 -2bc"  ),
  (  "41:cab",  "B 2 c b",  "B -2bc 2"  ),
  (  "41:-cba",  "C 2 c b",  "C -2bc 2"  ),
  (  "41:bca",  "C c 2 a",  "C -2bc -2bc"  ),
  (  "41:a-cb",  "A c 2 a",  "A -2ac -2ac"  ),
  (  "42",  "F m m 2",  "F 2 -2"  ),
  (  "42:cab",  "F 2 m m",  "F -2 2"  ),
  (  "42:bca",  "F m 2 m",  "F -2 -2"  ),
  (  "43",  "F d d 2",  "F 2 -2d"  ),
  (  "43:cab",  "F 2 d d",  "F -2d 2"  ),
  (  "43:bca",  "F d 2 d",  "F -2d -2d"  ),
  (  "44",  "I m m 2",  "I 2 -2"  ),
  (  "44:cab",  "I 2 m m",  "I -2 2"  ),
  (  "44:bca",  "I m 2 m",  "I -2 -2"  ),
  (  "45",  "I b a 2",  "I 2 -2c"  ),
  (  "45:cab",  "I 2 c b",  "I -2a 2"  ),
  (  "45:bca",  "I c 2 a",  "I -2b -2b"  ),
  (  "46",  "I m a 2",  "I 2 -2a"  ),
  (  "46:ba-c",  "I b m 2",  "I 2 -2b"  ),
  (  "46:cab",  "I 2 m b",  "I -2b 2"  ),
  (  "46:-cba",  "I 2 c m",  "I -2c 2"  ),
  (  "46:bca",  "I c 2 m",  "I -2c -2c"  ),
  (  "46:a-cb",  "I m 2 a",  "I -2a -2a"  ),
  (  "47",  "P m m m",  "-P 2 2"  ),
  (  "48:1",  "P n n n:1",  "P 2 2 -1n"  ),
  (  "48:2",  "P n n n:2",  "-P 2ab 2bc"  ),
  (  "49",  "P c c m",  "-P 2 2c"  ),
  (  "49:cab",  "P m a a",  "-P 2a 2"  ),
  (  "49:bca",  "P b m b",  "-P 2b 2b"  ),
  (  "50:1",  "P b a n:1",  "P 2 2 -1ab"  ),
  (  "50:2",  "P b a n:2",  "-P 2ab 2b"  ),
  (  "50:1cab",  "P n c b:1",  "P 2 2 -1bc"  ),
  (  "50:2cab",  "P n c b:2",  "-P 2b 2bc"  ),
  (  "50:1bca",  "P c n a:1",  "P 2 2 -1ac"  ),
  (  "50:2bca",  "P c n a:2",  "-P 2a 2c"  ),
  (  "51",  "P m m a",  "-P 2a 2a"  ),
  (  "51:ba-c",  "P m m b",  "-P 2b 2"  ),
  (  "51:cab",  "P b m m",  "-P 2 2b"  ),
  (  "51:-cba",  "P c m m",  "-P 2c 2c"  ),
  (  "51:bca",  "P m c m",  "-P 2c 2"  ),
  (  "51:a-cb",  "P m a m",  "-P 2 2a"  ),
  (  "52",  "P n n a",  "-P 2a 2bc"  ),
  (  "52:ba-c",  "P n n b",  "-P 2b 2n"  ),
  (  "52:cab",  "P b n n",  "-P 2n 2b"  ),
  (  "52:-cba",  "P c n n",  "-P 2ab 2c"  ),
  (  "52:bca",  "P n c n",  "-P 2ab 2n"  ),
  (  "52:a-cb",  "P n a n",  "-P 2n 2bc"  ),
  (  "53",  "P m n a",  "-P 2ac 2"  ),
  (  "53:ba-c",  "P n m b",  "-P 2bc 2bc"  ),
  (  "53:cab",  "P b m n",  "-P 2ab 2ab"  ),
  (  "53:-cba",  "P c n m",  "-P 2 2ac"  ),
  (  "53:bca",  "P n c m",  "-P 2 2bc"  ),
  (  "53:a-cb",  "P m a n",  "-P 2ab 2"  ),
  (  "54",  "P c c a",  "-P 2a 2ac"  ),
  (  "54:ba-c",  "P c c b",  "-P 2b 2c"  ),
  (  "54:cab",  "P b a a",  "-P 2a 2b"  ),
  (  "54:-cba",  "P c a a",  "-P 2ac 2c"  ),
  (  "54:bca",  "P b c b",  "-P 2bc 2b"  ),
  (  "54:a-cb",  "P b a b",  "-P 2b 2ab"  ),
  (  "55",  "P b a m",  "-P 2 2ab"  ),
  (  "55:cab",  "P m c b",  "-P 2bc 2"  ),
  (  "55:bca",  "P c m a",  "-P 2ac 2ac"  ),
  (  "56",  "P c c n",  "-P 2ab 2ac"  ),
  (  "56:cab",  "P n a a",  "-P 2ac 2bc"  ),
  (  "56:bca",  "P b n b",  "-P 2bc 2ab"  ),
  (  "57",  "P b c m",  "-P 2c 2b"  ),
  (  "57:ba-c",  "P c a m",  "-P 2c 2ac"  ),
  (  "57:cab",  "P m c a",  "-P 2ac 2a"  ),
  (  "57:-cba",  "P m a b",  "-P 2b 2a"  ),
  (  "57:bca",  "P b m a",  "-P 2a 2ab"  ),
  (  "57:a-cb",  "P c m b",  "-P 2bc 2c"  ),
  (  "58",  "P n n m",  "-P 2 2n"  ),
  (  "58:cab",  "P m n n",  "-P 2n 2"  ),
  (  "58:bca",  "P n m n",  "-P 2n 2n"  ),
  (  "59:1",  "P m m n:1",  "P 2 2ab -1ab"  ),
  (  "59:2",  "P m m n:2",  "-P 2ab 2a"  ),
  (  "59:1cab",  "P n m m:1",  "P 2bc 2 -1bc"  ),
  (  "59:2cab",  "P n m m:2",  "-P 2c 2bc"  ),
  (  "59:1bca",  "P m n m:1",  "P 2ac 2ac -1ac"  ),
  (  "59:2bca",  "P m n m:2",  "-P 2c 2a"  ),
  (  "60",  "P b c n",  "-P 2n 2ab"  ),
  (  "60:ba-c",  "P c a n",  "-P 2n 2c"  ),
  (  "60:cab",  "P n c a",  "-P 2a 2n"  ),
  (  "60:-cba",  "P n a b",  "-P 2bc 2n"  ),
  (  "60:bca",  "P b n a",  "-P 2ac 2b"  ),
  (  "60:a-cb",  "P c n b",  "-P 2b 2ac"  ),
  (  "61",  "P b c a",  "-P 2ac 2ab"  ),
  (  "61:ba-c",  "P c a b",  "-P 2bc 2ac"  ),
  (  "62",  "P n m a",  "-P 2ac 2n"  ),
  (  "62:ba-c",  "P m n b",  "-P 2bc 2a"  ),
  (  "62:cab",  "P b n m",  "-P 2c 2ab"  ),
  (  "62:-cba",  "P c m n",  "-P 2n 2ac"  ),
  (  "62:bca",  "P m c n",  "-P 2n 2a"  ),
  (  "62:a-cb",  "P n a m",  "-P 2c 2n"  ),
  (  "63",  "C m c m",  "-C 2c 2"  ),
  (  "63:ba-c",  "C c m m",  "-C 2c 2c"  ),
  (  "63:cab",  "A m m a",  "-A 2a 2a"  ),
  (  "63:-cba",  "A m a m",  "-A 2 2a"  ),
  (  "63:bca",  "B b m m",  "-B 2 2b"  ),
  (  "63:a-cb",  "B m m b",  "-B 2b 2"  ),
  (  "64",  "C m c a",  "-C 2bc 2"  ),
  (  "64:ba-c",  "C c m b",  "-C 2bc 2bc"  ),
  (  "64:cab",  "A b m a",  "-A 2ac 2ac"  ),
  (  "64:-cba",  "A c a m",  "-A 2 2ac"  ),
  (  "64:bca",  "B b c m",  "-B 2 2bc"  ),
  (  "64:a-cb",  "B m a b",  "-B 2bc 2"  ),
  (  "65",  "C m m m",  "-C 2 2"  ),
  (  "65:cab",  "A m m m",  "-A 2 2"  ),
  (  "65:bca",  "B m m m",  "-B 2 2"  ),
  (  "66",  "C c c m",  "-C 2 2c"  ),
  (  "66:cab",  "A m a a",  "-A 2a 2"  ),
  (  "66:bca",  "B b m b",  "-B 2b 2b"  ),
  (  "67",  "C m m a",  "-C 2b 2"  ),
  (  "67:ba-c",  "C m m b",  "-C 2b 2b"  ),
  (  "67:cab",  "A b m m",  "-A 2c 2c"  ),
  (  "67:-cba",  "A c m m",  "-A 2 2c"  ),
  (  "67:bca",  "B m c m",  "-B 2 2c"  ),
  (  "67:a-cb",  "B m a m",  "-B 2c 2"  ),
  (  "68:1",  "C c c a:1",  "C 2 2 -1bc"  ),
  (  "68:2",  "C c c a:2",  "-C 2b 2bc"  ),
  (  "68:1ba-c",  "C c c b:1",  "C 2 2 -1bc"  ),
  (  "68:2ba-c",  "C c c b:2",  "-C 2b 2c"  ),
  (  "68:1cab",  "A b a a:1",  "A 2 2 -1ac"  ),
  (  "68:2cab",  "A b a a:2",  "-A 2a 2c"  ),
  (  "68:1-cba",  "A c a a:1",  "A 2 2 -1ac"  ),
  (  "68:2-cba",  "A c a a:2",  "-A 2ac 2c"  ),
  (  "68:1bca",  "B b c b:1",  "B 2 2 -1bc"  ),
  (  "68:2bca",  "B b c b:2",  "-B 2bc 2b"  ),
  (  "68:1a-cb",  "B b a b:1",  "B 2 2 -1bc"  ),
  (  "68:2a-cb",  "B b a b:2",  "-B 2b 2bc"  ),
  (  "69",  "F m m m",  "-F 2 2"  ),
  (  "70:1",  "F d d d:1",  "F 2 2 -1d"  ),
  (  "70:2",  "F d d d:2",  "-F 2uv 2vw"  ),
  (  "71",  "I m m m",  "-I 2 2"  ),
  (  "72",  "I b a m",  "-I 2 2c"  ),
  (  "72:cab",  "I m c b",  "-I 2a 2"  ),
  (  "72:bca",  "I c m a",  "-I 2b 2b"  ),
  (  "73",  "I b c a",  "-I 2b 2c"  ),
  (  "73:ba-c",  "I c a b",  "-I 2a 2b"  ),
  (  "74",  "I m m a",  "-I 2b 2"  ),
  (  "74:ba-c",  "I m m b",  "-I 2a 2a"  ),
  (  "74:cab",  "I b m m",  "-I 2c 2c"  ),
  (  "74:-cba",  "I c m m",  "-I 2 2b"  ),
  (  "74:bca",  "I m c m",  "-I 2 2a"  ),
  (  "74:a-cb",  "I m a m",  "-I 2c 2"  ),
  (  "75",  "P 4",  "P 4"  ),
  (  "76",  "P 41",  "P 4w"  ),
  (  "77",  "P 42",  "P 4c"  ),
  (  "78",  "P 43",  "P 4cw"  ),
  (  "79",  "I 4",  "I 4"  ),
  (  "80",  "I 41",  "I 4bw"  ),
  (  "81",  "P -4",  "P -4"  ),
  (  "82",  "I -4",  "I -4"  ),
  (  "83",  "P 4/m",  "-P 4"  ),
  (  "84",  "P 42/m",  "-P 4c"  ),
  (  "85:1",  "P 4/n:1",  "P 4ab -1ab"  ),
  (  "85:2",  "P 4/n:2",  "-P 4a"  ),
  (  "86:1",  "P 42/n:1",  "P 4n -1n"  ),
  (  "86:2",  "P 42/n:2",  "-P 4bc"  ),
  (  "87",  "I 4/m",  "-I 4"  ),
  (  "88:1",  "I 41/a:1",  "I 4bw -1bw"  ),
  (  "88:2",  "I 41/a:2",  "-I 4ad"  ),
  (  "89",  "P 4 2 2",  "P 4 2"  ),
  (  "90",  "P 42 1 2",  "P 4ab 2ab"  ),
  (  "91",  "P 41 2 2",  "P 4w 2c"  ),
  (  "92",  "P 41 21 2",  "P 4abw 2nw"  ),
  (  "93",  "P 42 2 2",  "P 4c 2"  ),
  (  "94",  "P 42 21 2",  "P 4n 2n"  ),
  (  "95",  "P 43 2 2",  "P 4cw 2c"  ),
  (  "96",  "P 43 21 2",  "P 4nw 2abw"  ),
  (  "97",  "I 4 2 2",  "I 4 2"  ),
  (  "98",  "I 41 2 2",  "I 4bw 2bw"  ),
  (  "99",  "P 4 m m",  "P 4 -2"  ),
  (  "100",  "P 4 b m",  "P 4 -2ab"  ),
  (  "101",  "P 42 c m",  "P 4c -2c"  ),
  (  "102",  "P 42 n m",  "P 4n -2n"  ),
  (  "103",  "P 4 c c",  "P 4 -2c"  ),
  (  "104",  "P 4 n c",  "P 4 -2n"  ),
  (  "105",  "P 42 m c",  "P 4c -2"  ),
  (  "106",  "P 42 b c",  "P 4c -2ab"  ),
  (  "107",  "I 4 m m",  "I 4 -2"  ),
  (  "108",  "I 4 c m",  "I 4 -2c"  ),
  (  "109",  "I 41 m d",  "I 4bw -2"  ),
  (  "110",  "I 41 c d",  "I 4bw -2c"  ),
  (  "111",  "P -4 2 m",  "P -4 2"  ),
  (  "112",  "P -4 2 c",  "P -4 2c"  ),
  (  "113",  "P -4 21 m",  "P -4 2ab"  ),
  (  "114",  "P -4 21 c",  "P -4 2n"  ),
  (  "115",  "P -4 m 2",  "P -4 -2"  ),
  (  "116",  "P -4 c 2",  "P -4 -2c"  ),
  (  "117",  "P -4 b 2",  "P -4 -2ab"  ),
  (  "118",  "P -4 n 2",  "P -4 -2n"  ),
  (  "119",  "I -4 m 2",  "I -4 -2"  ),
  (  "120",  "I -4 c 2",  "I -4 -2c"  ),
  (  "121",  "I -4 2 m",  "I -4 2"  ),
  (  "122",  "I -4 2 d",  "I -4 2bw"  ),
  (  "123",  "P 4/m m m",  "-P 4 2"  ),
  (  "124",  "P 4/m c c",  "-P 4 2c"  ),
  (  "125:1",  "P 4/n b m:1",  "P 4 2 -1ab"  ),
  (  "125:2",  "P 4/n b m:2",  "-P 4a 2b"  ),
  (  "126:1",  "P 4/n n c:1",  "P 4 2 -1n"  ),
  (  "126:2",  "P 4/n n c:2",  "-P 4a 2bc"  ),
  (  "127",  "P 4/m b m",  "-P 4 2ab"  ),
  (  "128",  "P 4/m n c",  "-P 4 2n"  ),
  (  "129:1",  "P 4/n m m:1",  "P 4ab 2ab -1ab"  ),
  (  "129:2",  "P 4/n m m:2",  "-P 4a 2a"  ),
  (  "130:1",  "P 4/n c c:1",  "P 4ab 2n -1ab"  ),
  (  "130:2",  "P 4/n c c:2",  "-P 4a 2ac"  ),
  (  "131",  "P 42/m m c",  "-P 4c 2"  ),
  (  "132",  "P 42/m c m",  "-P 4c 2c"  ),
  (  "133:1",  "P 42/n b c:1",  "P 4n 2c -1n"  ),
  (  "133:2",  "P 42/n b c:2",  "-P 4ac 2b"  ),
  (  "134:1",  "P 42/n n m:1",  "P 4n 2 -1n"  ),
  (  "134:2",  "P 42/n n m:2",  "-P 4ac 2bc"  ),
  (  "135",  "P 42/m b c",  "-P 4c 2ab"  ),
  (  "136",  "P 42/m n m",  "-P 4n 2n"  ),
  (  "137:1",  "P 42/n m c:1",  "P 4n 2n -1n"  ),
  (  "137:2",  "P 42/n m c:2",  "-P 4ac 2a"  ),
  (  "138:1",  "P 42/n c m:1",  "P 4n 2ab -1n"  ),
  (  "138:2",  "P 42/n c m:2",  "-P 4ac 2ac"  ),
  (  "139",  "I 4/m m m",  "-I 4 2"  ),
  (  "140",  "I 4/m c m",  "-I 4 2c"  ),
  (  "141:1",  "I 41/a m d:1",  "I 4bw 2bw -1bw"  ),
  (  "141:2",  "I 41/a m d:2",  "-I 4bd 2"  ),
  (  "142:1",  "I 41/a c d:1",  "I 4bw 2aw -1bw"  ),
  (  "142:2",  "I 41/a c d:2",  "-I 4bd 2c"  ),
  (  "143",  "P 3",  "P 3"  ),
  (  "144",  "P 31",  "P 31"  ),
  (  "145",  "P 32",  "P 32"  ),
  (  "146:H",  "R 3:H",  "R 3"  ),
  (  "146:R",  "R 3:R",  "P 3*"  ),
  (  "147",  "P -3",  "-P 3"  ),
  (  "148:H",  "R -3:H",  "-R 3"  ),
  (  "148:R",  "R -3:R",  "-P 3*"  ),
  (  "149",  "P 3 1 2",  "P 3 2"  ),
  (  "150",  "P 3 2 1",  "P 3 2\""  ),
  (  "151",  "P 31 1 2",  "P 31 2c (0 0 1)"  ),
  (  "152",  "P 31 2 1",  "P 31 2\""  ),
  (  "153",  "P 32 1 2",  "P 32 2c (0 0 -1)"  ),
  (  "154",  "P 32 2 1",  "P 32 2\""  ),
  (  "155:H",  "R 3 2:H",  "R 3 2\""  ),
  (  "155:R",  "R 3 2:R",  "P 3* 2"  ),
  (  "156",  "P 3 m 1",  "P 3 -2\""  ),
  (  "157",  "P 3 1 m",  "P 3 -2"  ),
  (  "158",  "P 3 c 1",  "P 3 -2\"c"  ),
  (  "159",  "P 3 1 c",  "P 3 -2c"  ),
  (  "160:H",  "R 3 m:H",  "R 3 -2\""  ),
  (  "160:R",  "R 3 m:R",  "P 3* -2"  ),
  (  "161:H",  "R 3 c:H",  "R 3 -2\"c"  ),
  (  "161:R",  "R 3 c:R",  "P 3* -2n"  ),
  (  "162",  "P -3 1 m",  "-P 3 2"  ),
  (  "163",  "P -3 1 c",  "-P 3 2c"  ),
  (  "164",  "P -3 m 1",  "-P 3 2\""  ),
  (  "165",  "P -3 c 1",  "-P 3 2\"c"  ),
  (  "166:H",  "R -3 m:H",  "-R 3 2\""  ),
  (  "166:R",  "R -3 m:R",  "-P 3* 2"  ),
  (  "167:H",  "R -3 c:H",  "-R 3 2\"c"  ),
  (  "167:R",  "R -3 c:R",  "-P 3* 2n"  ),
  (  "168",  "P 6",  "P 6"  ),
  (  "169",  "P 61",  "P 61"  ),
  (  "170",  "P 65",  "P 65"  ),
  (  "171",  "P 62",  "P 62"  ),
  (  "172",  "P 64",  "P 64"  ),
  (  "173",  "P 63",  "P 6c"  ),
  (  "174",  "P -6",  "P -6"  ),
  (  "175",  "P 6/m",  "-P 6"  ),
  (  "176",  "P 63/m",  "-P 6c"  ),
  (  "177",  "P 6 2 2",  "P 6 2"  ),
  (  "178",  "P 61 2 2",  "P 61 2 (0 0 -1)"  ),
  (  "179",  "P 65 2 2",  "P 65 2 (0 0 1)"  ),
  (  "180",  "P 62 2 2",  "P 62 2c (0 0 1)"  ),
  (  "181",  "P 64 2 2",  "P 64 2c (0 0 -1)"  ),
  (  "182",  "P 63 2 2",  "P 6c 2c"  ),
  (  "183",  "P 6 m m",  "P 6 -2"  ),
  (  "184",  "P 6 c c",  "P 6 -2c"  ),
  (  "185",  "P 63 c m",  "P 6c -2"  ),
  (  "186",  "P 63 m c",  "P 6c -2c"  ),
  (  "187",  "P -6 m 2",  "P -6 2"  ),
  (  "188",  "P -6 c 2",  "P -6c 2"  ),
  (  "189",  "P -6 2 m",  "P -6 -2"  ),
  (  "190",  "P -6 2 c",  "P -6c -2c"  ),
  (  "191",  "P 6/m m m",  "-P 6 2"  ),
  (  "192",  "P 6/m c c",  "-P 6 2c"  ),
  (  "193",  "P 63/m c m",  "-P 6c 2"  ),
  (  "194",  "P 63/m m c",  "-P 6c 2c"  ),
  (  "195",  "P 2 3",  "P 2 2 3"  ),
  (  "196",  "F 2 3",  "F 2 2 3"  ),
  (  "197",  "I 2 3",  "I 2 2 3"  ),
  (  "198",  "P 21 3",  "P 2ac 2ab 3"  ),
  (  "199",  "I 21 3",  "I 2b 2c 3"  ),
  (  "200",  "P m -3",  "-P 2 2 3"  ),
  (  "201:1",  "P n -3:1",  "P 2 2 3 -1n"  ),
  (  "201:2",  "P n -3:2",  "-P 2ab 2bc 3"  ),
  (  "202",  "F m -3",  "-F 2 2 3"  ),
  (  "203:1",  "F d -3:1",  "F 2 2 3 -1d"  ),
  (  "203:2",  "F d -3:2",  "-F 2uv 2vw 3"  ),
  (  "204",  "I m -3",  "-I 2 2 3"  ),
  (  "205",  "P a -3",  "-P 2ac 2ab 3"  ),
  (  "206",  "I a -3",  "-I 2b 2c 3"  ),
  (  "207",  "P 4 3 2",  "P 4 2 3"  ),
  (  "208",  "P 42 3 2",  "P 4n 2 3"  ),
  (  "209",  "F 4 3 2",  "F 4 2 3"  ),
  (  "210",  "F 41 3 2",  "F 4d 2 3"  ),
  (  "211",  "I 4 3 2",  "I 4 2 3"  ),
  (  "212",  "P 43 3 2",  "P 4acd 2ab 3"  ),
  (  "213",  "P 41 3 2",  "P 4bd 2ab 3"  ),
  (  "214",  "I 41 3 2",  "I 4bd 2c 3"  ),
  (  "215",  "P -4 3 m",  "P -4 2 3"  ),
  (  "216",  "F -4 3 m",  "F -4 2 3"  ),
  (  "217",  "I -4 3 m",  "I -4 2 3"  ),
  (  "218",  "P -4 3 n",  "P -4n 2 3"  ),
  (  "219",  "F -4 3 c",  "F -4c 2 3"  ),
  (  "220",  "I -4 3 d",  "I -4bd 2c 3"  ),
  (  "221",  "P m -3 m",  "-P 4 2 3"  ),
  (  "222:1",  "P n -3 n:1",  "P 4 2 3 -1n"  ),
  (  "222:2",  "P n -3 n:2",  "-P 4a 2bc 3"  ),
  (  "223",  "P m -3 n",  "-P 4n 2 3"  ),
  (  "224:1",  "P n -3 m:1",  "P 4n 2 3 -1n"  ),
  (  "224:2",  "P n -3 m:2",  "-P 4bc 2bc 3"  ),
  (  "225",  "F m -3 m",  "-F 4 2 3"  ),
  (  "226",  "F m -3 c",  "-F 4c 2 3"  ),
  (  "227:1",  "F d -3 m:1",  "F 4d 2 3 -1d"  ),
  (  "227:2",  "F d -3 m:2",  "-F 4vw 2vw 3"  ),
  (  "228:1",  "F d -3 c:1",  "F 4d 2 3 -1cd"  ),
  (  "228:2",  "F d -3 c:2",  "-F 4cvw 2vw 3"  ),
  (  "229",  "I m -3 m",  "-I 4 2 3"  ),
  (  "230",  "I a -3 d",  "-I 4bd 2c 3"  )
  ]